ORTHOGONAL POLYNOMIAL INFERENCE METHOD OF THE PROBABILITY DISTRIBUTION FUNCTION FOR SMALL SAMPLES OF GEOTECHNICAL PARAMETERS

Geotechnical parameters obtained in engineering practice are usually small samples, and the typical probability distributions such as normal distribution, logarithmic normal distribution, beta distribution and Weibull distribution were used to fit their optimal probability models in general. However, three basic problems have not been solved in the aforementioned inference, including the unmatched integral interval of sample distribution, the selection in limited range and that single peak probability distribution function cannot reflect the random fluctuation of parameters. To investigate these three problems, five different intervals were selected firstly, and Legendre polynomial and Chebyshev polynomial of the second class were used to infer the probability distribution function of 10 groups of geotechnical parameters. The K-S method was used to test the optimal property of the thus-obtained probability functions. Through the comparison of the interval value matching, fitting test values and cumulative probability values, a new integral interval standard that combines 3σ principle and the effect of skewness was put forward. The results also show that the order of the optimal probability distribution can be determined by the finite comparison method, and all the test values of orthogonal polynomial inference method are smaller than that of traditional method. The optimal probability distribution can reflect the random fluctuation of small sample data, which is more accordant with the actual conditions for geotechnical parameters.